This paper studies the effects of immigration on health. We merge information on individual characteristics from the German Socio-Economic Panel (1984-2010) with detailed local labour market characteristics and exploit the longitudinal component of the data to analyse how immigration affects the health of both immigrants and natives over time. Upon their arrival, immigrants are found to be healthier than the natives (healthy immigrant effect), but their health deteriorates over time spent in Germany. We show that the convergence in health is heterogeneous across immigrants and occurs more rapidly among those working in more physically demanding jobs. Immigrants are significantly more likely to work in strenuous occupations. In light of these facts, we investigate whether changes in the spatial concentration of immigrants affect the health of the native population. Our results suggest that immigration reduces the likelihood that residents report negative health outcomes. We show that these effects are concentrated in blue-collar occupations and are larger among low educated natives and previous cohorts of immigrants. The improvement in the average working conditions and workload of natives contributes to explain the positive effect of immigration on the health of the native population.